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A periodic Levinson-Durbin algorithm for entropy maximization

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  • Boshnakov, Georgi N.
  • Lambert-Lacroix, Sophie

Abstract

A recursive algorithm is presented for the computation of the first-order and second-order derivatives of the entropy of a periodic autoregressive process with respect to the autocovariances. It is an extension of the periodic Levinson-Durbin algorithm. The algorithm has been developed for use at one of the steps of an entropy maximization method developed by the authors. Numerical examples of entropy maximization by that method are given. An implementation of the algorithm is available as an R package.

Suggested Citation

  • Boshnakov, Georgi N. & Lambert-Lacroix, Sophie, 2012. "A periodic Levinson-Durbin algorithm for entropy maximization," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 15-24, January.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:1:p:15-24
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    1. Hindrayanto, Irma & Koopman, Siem Jan & Ooms, Marius, 2010. "Exact maximum likelihood estimation for non-stationary periodic time series models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2641-2654, November.
    2. Castro, Glaysar & Girardin, Valerie, 2002. "Maximum of entropy and extension of covariance matrices for periodically correlated and multivariate processes," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 37-52, August.
    3. Georgi N. Boshnakov & Sophie Lambert‐Lacroix, 2009. "Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(5), pages 467-486, September.
    4. Sophie Lambert‐Lacroix, 2005. "Extension of Autocovariance Coefficients Sequence for Periodically Correlated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 423-435, May.
    5. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
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    1. Bos, Charles S. & Koopman, Siem Jan & Ooms, Marius, 2014. "Long memory with stochastic variance model: A recursive analysis for US inflation," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 144-157.

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